Season the chicken breasts with salt and pepper. Heat olive oil in a skillet over medium-high heat, sear chicken for 5-6 minutes until golden. Transfer to a plate to cool.

In the same skillet, melt butter, then add mushrooms, shallots, and garlic. Sauté for 8-10 minutes until tender, then cool fully.

Layer prosciutto on plastic wrap, spread cooled duxelles over it, place chicken on top, roll tightly into a log shape using the wrap, and chill for 15-20 minutes.

Preheat oven to 400°F (200°C). Roll out puff pastry, place the chicken log in the center, fold pastry over, seal edges with water, and chill for 10 minutes.

Brush pastry with egg wash, cut slits for steam, and bake for 25-30 minutes until golden brown. Let rest for 5 minutes before slicing.